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Up to CorrelationsWith35Percent in eop/independence
This commit is contained in:
Grant Sanderson
parent
62a7df7075
commit
029c4f3c1f
1 changed files with 620 additions and 11 deletions
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@ -83,21 +83,37 @@ def get_slot_group(bool_list, buff = MED_LARGE_BUFF, include_qs = True):
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base = 2.3
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for i, line in enumerate(lines):
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if i < len(bool_list):
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if bool_list[i]:
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mob = TexMobject("\\checkmark")
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mob.highlight(GREEN)
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slot_group.shift(total_height*DOWN / (base**(i+1)))
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else:
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mob = TexMobject("\\times")
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mob.highlight(RED)
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slot_group.shift(total_height*UP / (base**(i+1)))
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else:
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if i >= len(bool_list) or bool_list[i] is None:
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mob = VectorizedPoint()
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elif bool_list[i]:
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mob = TexMobject("\\checkmark")
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mob.highlight(GREEN)
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slot_group.shift(total_height*DOWN / (base**(i+1)))
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else:
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mob = TexMobject("\\times")
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mob.highlight(RED)
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slot_group.shift(total_height*UP / (base**(i+1)))
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mob.next_to(line, UP, SMALL_BUFF)
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slot_group.content.add(mob)
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return slot_group
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def get_probability_of_slot_group(bool_list, conditioned_list = None):
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filler_tex = "Filler"
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if conditioned_list is None:
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result = TexMobject("P(", filler_tex, ")")
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else:
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result = TexMobject("P(", filler_tex, "|", filler_tex, ")")
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fillers = result.get_parts_by_tex(filler_tex)
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for filler, bl in zip(fillers, [bool_list, conditioned_list]):
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slot_group = get_slot_group(
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bl, buff = SMALL_BUFF, include_qs = False,
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)
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slot_group.replace(filler, dim_to_match = 0)
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slot_group.shift(0.5*SMALL_BUFF*DOWN)
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index = result.index_of_part(filler)
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result.submobjects[index] = slot_group
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return result
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#########
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@ -339,7 +355,7 @@ class IntroduceBinomial(Scene):
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self.bar_chart = chart
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self.play(LaggedStart(
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FadeIn, VGroup(*chart.family_members_with_points()),
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FadeIn, VGroup(*it.chain(*chart)),
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run_time = 2
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))
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@ -1422,6 +1438,599 @@ class ShowIndependenceSymbolically(Scene):
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self.play(Transform(condition, slot_group))
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self.dither()
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class ComputeProbabilityOfOneWrong(Scene):
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CONFIG = {
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"score" : 2,
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"final_result_rhs_tex" : [
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"3", "(0.8)", "^2", "(0.2)", "=", "0.384",
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],
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"default_bool" : True,
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"default_p" : "0.8",
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"default_q" : "0.2",
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}
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def construct(self):
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self.show_all_three_patterns()
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self.show_final_result()
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def show_all_three_patterns(self):
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probabilities = VGroup()
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point_8s = VGroup()
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point_2s = VGroup()
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for i in reversed(range(3)):
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bool_list = [self.default_bool]*3
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bool_list[i] = not self.default_bool
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probs = ["(%s)"%self.default_p]*3
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probs[i] = "(%s)"%self.default_q
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lhs = get_probability_of_slot_group(bool_list)
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rhs = TexMobject("=", *probs)
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rhs.highlight_by_tex("0.8", GREEN)
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rhs.highlight_by_tex("0.2", RED)
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point_8s.add(*rhs.get_parts_by_tex("0.8"))
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point_2s.add(*rhs.get_parts_by_tex("0.2"))
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rhs.next_to(lhs, RIGHT)
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probabilities.add(VGroup(lhs, rhs))
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probabilities.arrange_submobjects(DOWN, buff = LARGE_BUFF)
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probabilities.center()
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self.play(Write(probabilities[0]))
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self.dither(2)
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for i in range(2):
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self.play(ReplacementTransform(
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probabilities[i].copy(),
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probabilities[i+1]
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))
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self.dither()
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for group in point_8s, point_2s:
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self.play(LaggedStart(
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Indicate, group,
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rate_func = there_and_back,
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lag_ratio = 0.7
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))
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self.dither()
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def show_final_result(self):
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result = TexMobject(
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"P(", "\\text{Score} = %s"%self.score, ")", "=",
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*self.final_result_rhs_tex
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)
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result.highlight_by_tex_to_color_map({
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"0.8" : GREEN,
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"0.2" : RED,
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"Score" : YELLOW,
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})
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result[-1].highlight(YELLOW)
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result.highlight_by_tex("0.8", GREEN)
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result.highlight_by_tex("0.2", RED)
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result.to_edge(UP)
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self.play(Write(result))
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self.dither()
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class ComputeProbabilityOfOneRight(ComputeProbabilityOfOneWrong):
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CONFIG = {
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"score" : 1,
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"final_result_rhs_tex" : [
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"3", "(0.8)", "(0.2)", "^2", "=", "0.096",
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],
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"default_bool" : False,
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"default_p" : "0.2",
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"default_q" : "0.8",
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}
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class ShowFullDistribution(Scene):
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def construct(self):
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self.add_scores_one_and_two()
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self.add_scores_zero_and_three()
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self.show_bar_chart()
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self.compare_to_binomial_pattern()
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self.show_alternate_values_of_p()
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def add_scores_one_and_two(self):
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scores = VGroup(
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TexMobject(
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"P(", "\\text{Score} = 0", ")",
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"=", "(0.2)", "^3",
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"=", "0.008",
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),
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TexMobject(
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"P(", "\\text{Score} = 1", ")",
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"=", "3", "(0.8)", "(0.2)", "^2",
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"=", "0.096",
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),
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TexMobject(
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"P(", "\\text{Score} = 2", ")",
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"=", "3", "(0.8)", "^2", "(0.2)",
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"=", "0.384",
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),
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TexMobject(
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"P(", "\\text{Score} = 3", ")",
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"=", "(0.8)", "^3",
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"=", "0.512",
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),
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)
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scores.arrange_submobjects(
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DOWN,
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buff = MED_LARGE_BUFF,
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aligned_edge = LEFT
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)
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scores.shift(MED_LARGE_BUFF*UP)
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scores.to_edge(LEFT)
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for score in scores:
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score.highlight_by_tex_to_color_map({
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"0.8" : GREEN,
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"0.2" : RED,
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})
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score[-1].highlight(YELLOW)
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self.add(*scores[1:3])
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self.scores = scores
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def add_scores_zero_and_three(self):
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self.p_slot_groups = VGroup()
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self.dither()
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self.add_edge_score(0, UP, False)
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self.add_edge_score(3, DOWN, True)
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def add_edge_score(self, index, vect, q_bool):
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score = self.scores[index]
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prob = VGroup(*score[:3])
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brace = Brace(prob, vect)
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p_slot_group = get_probability_of_slot_group([q_bool]*3)
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p_slot_group.next_to(brace, vect)
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group = VGroup(*it.chain(p_slot_group, brace, score))
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self.play(LaggedStart(
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FadeIn, group,
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run_time = 2,
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lag_ratio = 0.7,
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))
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self.dither(2)
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self.p_slot_groups.add(brace, p_slot_group)
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def show_bar_chart(self):
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p_terms = VGroup()
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to_fade = VGroup(self.p_slot_groups)
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value_mobs = VGroup()
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for score in self.scores:
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p_terms.add(VGroup(*score[:3]))
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to_fade.add(VGroup(*score[3:-1]))
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value_mobs.add(score[-1])
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dist = get_binomial_distribution(3, 0.8)
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values = map(dist, range(4))
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chart = BarChart(
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values, bar_names = range(4),
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)
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chart.shift(DOWN)
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new_p_terms = VGroup(*[
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TexMobject("P(", "S=%d"%k, ")")
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for k in range(4)
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])
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for term, bar in zip(new_p_terms, chart.bars):
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term[1].highlight(YELLOW)
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term.scale_to_fit_width(1.5*bar.get_width())
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term.next_to(bar, UP)
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self.play(
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ReplacementTransform(
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value_mobs, chart.bars,
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submobject_mode = "lagged_start",
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run_time = 2
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)
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)
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self.play(
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LaggedStart(FadeIn, VGroup(*it.chain(*[
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submob
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for submob in chart
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if submob is not chart.bars
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]))),
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Transform(p_terms, new_p_terms),
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FadeOut(to_fade),
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)
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self.dither(2)
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chart.bar_top_labels = p_terms
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chart.add(p_terms)
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self.bar_chart = chart
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def compare_to_binomial_pattern(self):
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dist = get_binomial_distribution(3, 0.5)
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values = map(dist, range(4))
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alt_chart = BarChart(values)
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alt_chart.move_to(self.bar_chart)
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bars = alt_chart.bars
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bars.set_fill(GREY, opacity = 0.5)
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vect = 4*UP
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bars.shift(vect)
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nums = VGroup(*map(TexMobject, map(str, [1, 3, 3, 1])))
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for num, bar in zip(nums, bars):
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num.next_to(bar, UP)
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bars_copy = bars.copy()
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self.play(
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LaggedStart(FadeIn, bars),
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LaggedStart(FadeIn, nums),
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)
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self.dither(2)
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self.play(bars_copy.shift, -vect)
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self.play(ReplacementTransform(
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bars_copy, self.bar_chart.bars
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))
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self.dither(2)
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self.play(
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VGroup(self.bar_chart, bars, nums).to_edge, LEFT
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)
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self.alt_bars = bars
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self.alt_bars_labels = nums
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def show_alternate_values_of_p(self):
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new_prob = TexMobject(
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"P(", "\\text{Correct}", ")", "=", "0.8"
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)
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new_prob.highlight_by_tex("Correct", GREEN)
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new_prob.shift(SPACE_WIDTH*RIGHT/2)
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new_prob.to_edge(UP)
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alt_ps = 0.5, 0.65, 0.25
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alt_rhss = VGroup()
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alt_charts = VGroup()
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for p in alt_ps:
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rhs = TexMobject(str(p))
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rhs.highlight(YELLOW)
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rhs.move_to(new_prob[-1])
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alt_rhss.add(rhs)
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dist = get_binomial_distribution(3, p)
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values = map(dist, range(4))
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chart = self.bar_chart.copy()
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chart.change_bar_values(values)
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for label, bar in zip(chart.bar_top_labels, chart.bars):
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label.next_to(bar, UP)
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alt_charts.add(chart)
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self.play(FadeIn(new_prob))
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self.play(Transform(new_prob[-1], alt_rhss[0]))
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point_5_probs = self.show_point_5_probs(new_prob)
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self.dither()
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self.play(Transform(self.bar_chart, alt_charts[0]))
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self.dither()
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self.play(FadeOut(point_5_probs))
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for rhs, chart in zip(alt_rhss, alt_charts)[1:]:
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self.play(Transform(new_prob[-1], rhs))
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self.play(Transform(self.bar_chart, chart))
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self.dither(2)
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def show_point_5_probs(self, mob):
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probs = VGroup()
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last = mob
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for k in range(4):
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buff = MED_LARGE_BUFF
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for indices in it.combinations(range(3), k):
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bool_list = np.array([False]*3)
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bool_list[list(indices)] = True
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prob = get_probability_of_slot_group(bool_list)
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rhs = TexMobject("= (0.5)^3")
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rhs.next_to(prob, RIGHT)
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prob.add(rhs)
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prob.scale(0.9)
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prob.next_to(last, DOWN, buff)
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probs.add(prob)
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last = prob
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buff = SMALL_BUFF
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self.play(LaggedStart(FadeIn, probs))
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self.dither()
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return probs
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class ProbablyWrong(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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"Probably wrong!",
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run_time = 1,
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)
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self.change_student_modes(
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*["angry"]*3,
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run_time = 1
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)
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self.dither()
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class ShowTrueDistribution(PiCreatureScene):
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def construct(self):
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self.remove(self.randy)
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self.add_title()
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self.show_distributions()
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self.show_emotion()
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self.imagine_score_0()
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def add_title(self):
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title = TexMobject("P(", "\\text{Correct}", ")", "=", "0.65")
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title.to_edge(UP)
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title.highlight_by_tex("Correct", GREEN)
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self.add(title)
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self.title = title
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def show_distributions(self):
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dist = get_binomial_distribution(3, 0.65)
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values = np.array(map(dist, range(4)))
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alt_values = values + [0.2, 0, 0, 0.2]
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alt_values /= sum(alt_values)
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chart = BarChart(values, bar_names = range(4))
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bars = chart.bars
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old_bars = bars.copy()
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arrows = VGroup()
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for bar, old_bar in zip(bars, old_bars):
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for mob, vect in (bar, RIGHT), (old_bar, LEFT):
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mob.generate_target()
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mob.target.do_about_point(
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mob.get_corner(DOWN+vect),
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mob.target.stretch, 0.5, 0
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)
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old_bar.target.highlight(average_color(RED_E, BLACK))
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old_bar.target.set_stroke(width = 0)
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arrow = Arrow(ORIGIN, UP, buff = 0, color = GREEN)
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arrow.move_to(bar.get_bottom())
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arrow.shift(3*UP)
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arrows.add(arrow)
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for arrow in arrows[1:3]:
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arrow.rotate_in_place(np.pi)
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arrow.highlight(RED)
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arrows.gradient_highlight(BLUE, YELLOW)
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self.add(chart)
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self.play(*map(MoveToTarget, it.chain(bars, old_bars)))
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self.play(
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chart.change_bar_values, alt_values,
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*map(ShowCreation, arrows)
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)
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self.dither(2)
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self.bar_chart = chart
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self.old_bars = old_bars
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def show_emotion(self):
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randy = self.randy
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self.play(FadeIn(randy))
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self.play(randy.change, "sad")
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self.play(Blink(randy))
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def imagine_score_0(self):
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prob_rect = SurroundingRectangle(self.title[-1])
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bar_rect = SurroundingRectangle(VGroup(
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self.bar_chart.bars[0], self.old_bars[0],
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self.bar_chart.bar_labels[0],
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))
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self.play(ShowCreation(prob_rect))
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self.dither()
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self.play(ReplacementTransform(
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prob_rect, bar_rect
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))
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self.dither()
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self.play(FadeOut(bar_rect))
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#####
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def create_pi_creature(self):
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self.randy = Randolph()
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self.randy.to_corner(DOWN+LEFT)
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return self.randy
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class TeacherAssessingLiklihoodOfZero(TeacherStudentsScene):
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def construct(self):
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self.add_title()
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self.fade_other_students()
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self.show_independence_probability()
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self.teacher_reacts()
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def add_title(self):
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title = TexMobject("P(", "\\text{Correct}", ")", "=", "0.65")
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title.to_edge(UP)
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title.highlight_by_tex("Correct", GREEN)
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q_mark = TexMobject("?")
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q_mark.next_to(title[-2], UP, SMALL_BUFF)
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title.add(q_mark)
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self.add(title)
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self.title = title
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def fade_other_students(self):
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for student in self.students[0::2]:
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||||
student.fade(0.7)
|
||||
self.pi_creatures.remove(student)
|
||||
|
||||
def show_independence_probability(self):
|
||||
prob = get_probability_of_slot_group(3*[False])
|
||||
rhs = TexMobject("=", "(0.35)", "^3", "\\approx 4.3\\%")
|
||||
rhs.highlight_by_tex("0.35", RED)
|
||||
rhs.next_to(prob, RIGHT)
|
||||
prob.add(rhs)
|
||||
prob.next_to(self.teacher, UP+LEFT)
|
||||
words = TextMobject("Assuming independence")
|
||||
words.next_to(prob, UP)
|
||||
|
||||
self.play(
|
||||
self.teacher.change, "raise_right_hand",
|
||||
FadeIn(words),
|
||||
Write(prob)
|
||||
)
|
||||
self.dither()
|
||||
|
||||
self.ind_group = VGroup(prob, words)
|
||||
|
||||
def teacher_reacts(self):
|
||||
ind_group = self.ind_group
|
||||
box = SurroundingRectangle(ind_group)
|
||||
box.set_stroke(WHITE, 0)
|
||||
ind_group.add(box)
|
||||
ind_group.generate_target()
|
||||
ind_group.target.scale(0.7)
|
||||
ind_group.target.to_corner(UP+RIGHT, MED_SMALL_BUFF)
|
||||
ind_group.target[-1].set_stroke(WHITE, 2)
|
||||
|
||||
randy = self.students[1]
|
||||
|
||||
self.teacher_says(
|
||||
"Highly unlikely",
|
||||
target_mode = "sassy",
|
||||
added_anims = [MoveToTarget(ind_group)],
|
||||
run_time = 2,
|
||||
)
|
||||
self.play(randy.change, "sad")
|
||||
self.dither(2)
|
||||
self.play(
|
||||
RemovePiCreatureBubble(
|
||||
self.teacher, target_mode = "guilty",
|
||||
),
|
||||
PiCreatureSays(randy, "Wait!", target_mode = "surprised"),
|
||||
run_time = 1
|
||||
)
|
||||
self.dither(1)
|
||||
|
||||
class CorrelationsWith35Percent(ThousandPossibleQuizzes):
|
||||
def construct(self):
|
||||
self.add_top_calculation()
|
||||
self.show_first_split()
|
||||
self.show_second_split()
|
||||
self.show_third_split()
|
||||
self.comment_on_final_size()
|
||||
|
||||
def add_top_calculation(self):
|
||||
equation = VGroup(
|
||||
get_probability_of_slot_group(3*[False]),
|
||||
TexMobject("="),
|
||||
get_probability_of_slot_group([False]),
|
||||
get_probability_of_slot_group(2*[False], [False]),
|
||||
get_probability_of_slot_group(3*[False], 2*[False]),
|
||||
)
|
||||
equation.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
|
||||
equation.to_edge(UP)
|
||||
|
||||
self.add(equation)
|
||||
self.equation = equation
|
||||
|
||||
def show_first_split(self):
|
||||
quizzes = self.get_thousand_quizzes()
|
||||
n = int(0.65*len(quizzes))
|
||||
top_part = VGroup(*quizzes[:n])
|
||||
bottom_part = VGroup(*quizzes[n:])
|
||||
parts = [top_part, bottom_part]
|
||||
for part, color in zip(parts, [GREEN, RED]):
|
||||
part.generate_target()
|
||||
for quiz in part.target:
|
||||
quiz[0].highlight(color)
|
||||
top_part.target.shift(UP)
|
||||
brace = Brace(bottom_part, LEFT)
|
||||
prop = TexMobject("0.35")
|
||||
prop.next_to(brace, LEFT)
|
||||
|
||||
term = self.equation[2]
|
||||
term_brace = Brace(term, DOWN)
|
||||
|
||||
self.add(quizzes)
|
||||
self.dither()
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
FadeIn(prop),
|
||||
*map(MoveToTarget, parts)
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
top_part.fade, 0.8,
|
||||
Transform(brace, term_brace),
|
||||
prop.next_to, term_brace, DOWN,
|
||||
)
|
||||
self.dither()
|
||||
|
||||
self.quizzes = bottom_part
|
||||
self.quizzes.sort_submobjects(lambda p : p[0])
|
||||
|
||||
def show_second_split(self):
|
||||
n = int(0.45*len(self.quizzes))
|
||||
left_part = VGroup(*self.quizzes[:n])
|
||||
right_part = VGroup(*self.quizzes[n:])
|
||||
parts = [left_part, right_part]
|
||||
for part, color in zip(parts, [GREEN, RED_E]):
|
||||
part.generate_target()
|
||||
for quiz in part.target:
|
||||
quiz[1].highlight(color)
|
||||
left_part.target.shift(LEFT)
|
||||
brace = Brace(right_part, UP)
|
||||
prop = TexMobject(">0.35")
|
||||
prop.next_to(brace, UP)
|
||||
|
||||
term = self.equation[3]
|
||||
term_brace = Brace(term, DOWN)
|
||||
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
FadeIn(prop),
|
||||
*map(MoveToTarget, parts)
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
Transform(brace, term_brace),
|
||||
prop.next_to, term_brace, DOWN
|
||||
)
|
||||
self.play(left_part.fade, 0.8)
|
||||
|
||||
self.quizzes = right_part
|
||||
self.quizzes.sort_submobjects(lambda p : -p[1])
|
||||
|
||||
def show_third_split(self):
|
||||
quizzes = self.quizzes
|
||||
n = int(0.22*len(quizzes))
|
||||
top_part = VGroup(*quizzes[:n])
|
||||
bottom_part = VGroup(*quizzes[n:])
|
||||
parts = [top_part, bottom_part]
|
||||
for part, color in zip(parts, [GREEN, RED_B]):
|
||||
part.generate_target()
|
||||
for quiz in part.target:
|
||||
quiz[2].highlight(color)
|
||||
top_part.target.shift(0.5*UP)
|
||||
brace = Brace(bottom_part, LEFT)
|
||||
prop = TexMobject("\\gg 0.35")
|
||||
prop.next_to(brace, LEFT)
|
||||
|
||||
term = self.equation[4]
|
||||
term_brace = Brace(term, DOWN)
|
||||
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
FadeIn(prop),
|
||||
*map(MoveToTarget, parts)
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
Transform(brace, term_brace),
|
||||
prop.next_to, term_brace, DOWN,
|
||||
)
|
||||
self.play(top_part.fade, 0.8)
|
||||
self.dither()
|
||||
|
||||
self.quizzes = bottom_part
|
||||
|
||||
def comment_on_final_size(self):
|
||||
rect = SurroundingRectangle(self.quizzes)
|
||||
words = TextMobject(
|
||||
"Much more than ", "$(0.35)^3 \\approx 4.3\\%$"
|
||||
)
|
||||
words.next_to(rect, LEFT)
|
||||
|
||||
self.play(
|
||||
ShowCreation(rect),
|
||||
FadeIn(words)
|
||||
)
|
||||
self.dither()
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue